Characterization of the limit load in the case of an unbounded elastic convex
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, p. 637-648

In this work we consider a solid body Ω 3 constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces λf and a density of forces λg acting on the boundary where the real λ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by λ ¯ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995) 391-419]. Then assuming that the convex of elasticity at the point x of Ω, denoted by K(x), is written in the form of K D (x)+I, I is the identity of 9 sym , and the deviatoric component K D is bounded regardless of x Ω, we show under the condition “Rot f 0 or g is not colinear to the normal on a part of the boundary of Ω”, that the Limit Load λ ¯ searched is equal to the inverse of the infimum of the gauge of the Elastic convex translated by stress field equilibrating the unitary load corresponding to λ=1; moreover we show that this infimum is reached in a suitable function space.

DOI : https://doi.org/10.1051/m2an:2005028
Classification:  74xx
Keywords: elasticity, limit load
@article{M2AN_2005__39_4_637_0,
     author = {Elyacoubi, Adnene and Hadhri, Taieb},
     title = {Characterization of the limit load in the case of an unbounded elastic convex},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     pages = {637-648},
     doi = {10.1051/m2an:2005028},
     zbl = {pre02213933},
     mrnumber = {2165673},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_4_637_0}
}
Elyacoubi, Adnene; Hadhri, Taieb. Characterization of the limit load in the case of an unbounded elastic convex. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, pp. 637-648. doi : 10.1051/m2an:2005028. http://www.numdam.org/item/M2AN_2005__39_4_637_0/

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